Question

At a concession, five hot dogs and two hamburgers cost $12.00; two hot dogs and five hamburgers cost $14.25. Find the cost of one hot hot dog and the cost of one hamburger.

Answer 1

Answer : The cost of one hot hot dog and the cost of one hamburger is, $3.75

Step-by-step explanation :

Let the cost of hot dog be, 'x' and hamburger be, 'y'.

Given:

5 hot dogs and 2 hamburgers cost is, $12.00. The equation will be :

$5x+2y=12$           ..............(1)

2 hot dogs and 5 hamburgers cost is, $14.25. The equation will be :

$2x+5y=14.25$      ..............(2)

Now we have to determine the value of 'x' and 'y' by using substitution method.

$5x+2y=12$

$x=\frac{12-2y}{5}$       ............(3)

Now put equation 3 in 2, we get:

$2x+5y=14.25$

$2(\frac{12-2y}{5})+5y=14.25$

$\frac{24-4y}{5}+5y=14.25$

$24-4y+25y=71.25$

$21y=47.25$

y = 2.25

Now put the value of 'y' in 3, we get:

$x=\frac{12-2y}{5}$

$x=\frac{12-2(2.25)}{5}$

$x=\frac{12-4.5}{5}$

$x=\frac{7.5}{5}$

x = 1.5

Cost of hot dog = x = $1.5

Cost of hamburger = y = $2.25

Now we have to calculate the cost of one hot hot dog and the cost of one hamburger.

Cost of 1 hot hot dog and 1 hamburger = x + y

Cost of 1 hot hot dog and 1 hamburger = $1.5 + $2.25

Cost of 1 hot hot dog and 1 hamburger = $3.75

Therefore, the cost of one hot hot dog and the cost of one hamburger is, $3.75